Question

Katy has made her best affordable choice of noodles and iced tea. She spends all of her income on 15 packets of instant noodles at \(\$ 3\) each and 30 cups of iced tea at \(\$ 2\) each. Now the price of a packet of noodles rises to \(\$ 3.50\) per packet and the price of iced tea falls to \(\$ 1.75\) a cup. a. Will Katy now be able to consume 15 packets of instant noodles and 30 cups of iced tea? b. If Katy changes the quantities she buys, will she buy more or fewer packets of instant noodles? Explain your answer.

Short answer

Katy can still buy 15 packets of instant noodles and 30 cups of iced tea. She will not need to change the quantities she buys.

Step-by-step solution

Determine total initial spending

Calculate how much Katy initially spends on instant noodles and iced tea.15 packets of noodles at \(\$ 3\) each: 15 \times 3 = 4530 cups of iced tea at \(\$ 2\) each: 30 \times 2 = 60Total spending = \(45 + 60 = 105\)

Calculate new cost of noodles and iced tea

Calculate the total cost if buying the same quantities at the new prices:15 packets of noodles at \(\$ 3.5\) each:15 \times 3.5 = 52.530 cups of iced tea at \(\$ 1.75\) each:30 \times 1.75 = 52.5Total cost = \(52.5 + 52.5 = 105\)

Compare initial and new spending

Compare the initial total spending and the new total cost. Since both are \(\$ 105\), Katy can still afford the same quantities of noodles and iced tea.

Determine any change in quantities if necessary

Since the total cost remains the same and matches Katy's budget, no change in quantities is required. Thus, there is no need to buy more or fewer packets of instant noodles.

Key concepts

Consumer Choice

Consumer choice refers to the decisions that consumers make regarding the purchase of goods and services, based on their preferences, among various factors. People aim to maximize their utility (satisfaction) given their budget constraints. In Katy's case, she spends all her income on instant noodles and iced tea.

Initially, Katy's consumption choice includes 15 packets of instant noodles at \(3 each and 30 cups of iced tea at \)2 each, implying her preference for these quantities given her total income.

Consumers often face trade-offs and must decide which combination of goods will give the most satisfaction. For this, they consider relative prices of goods and their budget. Katy's choices reflect her aim to make the most out of her income by choosing an optimal combination of noodles and tea.

Changes in prices or income will alter the consumer's decision-making process. Changes in preferences or external factors could also influence these decisions.

Price Changes

Price changes can significantly affect a consumer's ability to afford the combination of goods they desire. When prices change, consumers need to reassess their budget constraints and reconsider their choices.

In Katy's scenario, the price of noodles rises from \(3 to \)3.50 per packet, and the price of iced tea falls from \(2 to \)1.75 per cup. Despite these changes, Katy’s total expenditure remains the same at \(105.

Here's a step-by-step look at the impact of these price changes:

• Katy initially spends \)45 on noodles (15 packets at \(3) and \)60 on iced tea (30 cups at \(2).
• At the new prices, she will spend \)52.5 on noodles (15 packets at \(3.50) and \)52.5 on iced tea (30 cups at \(1.75).

Despite the price change, the total spending remains \)105. This means that Katy can continue to buy the same quantities of noodles and iced tea without exceeding her budget, demonstrating how consumers adjust their spending to accommodate price variations.

Optimal Consumption Bundle

The concept of an optimal consumption bundle refers to the combination of goods that maximizes a consumer's utility, given their budget constraint. This is where they attain the highest satisfaction possible within their income limits.

For Katy, her optimal consumption bundle originally consists of 15 packets of instant noodles and 30 cups of iced tea. Following the price changes, the same consumption bundle remains optimal and affordable because her total expenditure of $105 does not change.

To determine whether Katy would buy more or fewer of either good after the price change, we compare the marginal utility per dollar spent. In Katy’s case, since total expenditure equals her budget before and after the price adjustments, she does not need to change the quantities she buys. She will continue to purchase 15 packets of noodles and 30 cups of iced tea.

This analysis shows that an optimal consumption bundle remains consistent when the total expenditure remains within the budget, even after price changes. The ultimate goal is to maximize utility while adhering to the budget constraint, adapting as needed to maintain an optimal mix of goods.